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71 lines
3.4 KiB
C++
71 lines
3.4 KiB
C++
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#ifndef MLPP_NUMERICAL_ANALYSIS_H
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#define MLPP_NUMERICAL_ANALYSIS_H
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//
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// NumericalAnalysis.hpp
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//
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//
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#include "core/math/math_defs.h"
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#include "core/object/reference.h"
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#include "core/containers/vector.h"
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#include "core/string/ustring.h"
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class MLPPVector;
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class MLPPMatrix;
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class MLPPTensor3;
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class MLPPNumericalAnalysis : public Reference {
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GDCLASS(MLPPNumericalAnalysis, Reference);
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public:
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/* A numerical method for derivatives is used. This may be subject to change,
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as an analytical method for calculating derivatives will most likely be used in
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the future.
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*/
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real_t num_diffr(real_t (*function)(real_t), real_t x);
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real_t num_diff_2r(real_t (*function)(real_t), real_t x);
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real_t num_diff_3r(real_t (*function)(real_t), real_t x);
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real_t constant_approximationr(real_t (*function)(real_t), real_t c);
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real_t linear_approximationr(real_t (*function)(real_t), real_t c, real_t x);
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real_t quadratic_approximationr(real_t (*function)(real_t), real_t c, real_t x);
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real_t cubic_approximationr(real_t (*function)(real_t), real_t c, real_t x);
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real_t num_diffv(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &, int axis);
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real_t num_diff_2v(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &, int axis1, int axis2);
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real_t num_diff_3v(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &, int axis1, int axis2, int axis3);
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real_t newton_raphson_method(real_t (*function)(real_t), real_t x_0, real_t epoch_num);
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real_t halley_method(real_t (*function)(real_t), real_t x_0, real_t epoch_num);
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real_t inv_quadratic_interpolation(real_t (*function)(real_t), const Ref<MLPPVector> &x_0, int epoch_num);
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real_t eulerian_methodr(real_t (*derivative)(real_t), real_t q_0, real_t q_1, real_t p, real_t h); // Euler's method for solving diffrential equations.
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real_t eulerian_methodv(real_t (*derivative)(const Ref<MLPPVector> &), real_t q_0, real_t q_1, real_t p, real_t h); // Euler's method for solving diffrential equations.
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real_t growth_method(real_t C, real_t k, real_t t); // General growth-based diffrential equations can be solved by seperation of variables.
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Ref<MLPPVector> jacobian(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &x); // Indeed, for functions with scalar outputs the Jacobians will be vectors.
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Ref<MLPPMatrix> hessian(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &x);
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Ref<MLPPTensor3> third_order_tensor(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &x);
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Vector<Ref<MLPPMatrix>> third_order_tensorvt(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &x);
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real_t constant_approximationv(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &c);
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real_t linear_approximationv(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &c, const Ref<MLPPVector> &x);
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real_t quadratic_approximationv(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &c, const Ref<MLPPVector> &x);
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real_t cubic_approximationv(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &c, const Ref<MLPPVector> &x);
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real_t laplacian(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &x); // laplacian
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String second_partial_derivative_test(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &x);
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protected:
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static void _bind_methods();
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};
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#endif /* NumericalAnalysis_hpp */
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